Existence of two limit cycles in Zeeman's class 30 for 3D Lotka-Volterra competitive system

DOI10.1007/S42967-022-00220-2OpenAlexW4308159273MaRDI QIDQ6085324

Yaoqi Li

Publication date: 12 December 2023

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42967-022-00220-2

zbMATH Keywords

limit cycleHopf bifurcationPoincaré-Bendixson theoremfine focus3-dimensional Lotka-Volterra (3D LV) competitive systemZeeman's class 30

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Cites Work

• Unnamed Item
• Four small limit cycles around a Hopf singular point in 3-dimensional competitive Lotka-Volterra systems
• On the number of limit cycles for three dimensional Lotka-Volterra systems
• On the first Lyapunov coefficient formula of 3D Lotka-Volterra equations with applications to multiplicity of limit cycles
• Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems

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